Question

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under such conditions, the density of $A$ is found to be 1.5 times the density of $B$. The ratio of molecular weight of $A$ and $B$ is

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $2$

Answer 1

The correct option is C $\frac{3}{4}$

For ideal gas, $PV=RT$ and $M=\rho V$
thus, $\frac{PM}{\rho }=RT$
here, $\frac{P_A{M}_A}{{\rho }_A}=RT....\left(1\right)$
and $\frac{P_B{M}_B}{{\rho }_B}=RT....\left(2\right)$
$\left(1\right)/\left(2\right)\Rightarrow \frac{M_A}{M_B}=\frac{{\rho }_A}{{\rho }_B}\times \frac{P_B}{P_A}$$=\frac{3}{2}\times \frac{1}{2}=\frac{3}{4}$